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2 years ago

Combine terms/simolify

Mathematics

1 answer:

-Dominant- [34]2 years ago

5 0

Answer:

$\dfrac{2m -1}{5}$

Step-by-step explanation:

Since we have common denominators inside the parentheses, we can combine the denominators. Then, we get the following expression:

$2\huge\text{(}\dfrac{1}{5} m - \dfrac{2}{5} \huge\text{)} + \dfrac{3}{5}$

$2\huge\text{(}\dfrac{m - 2}{5} \huge\text{)} + \dfrac{3}{5}$

Now, we can multiply the expression inside the parentheses by 2.

$\huge\text{(}\dfrac{2m - 4}{5} \huge\text{)} + \dfrac{3}{5}$

Since the expression inside the parentheses cannot be simplified further, we can open the parentheses and simplify the expression.

$\dfrac{2m - 4}{5} + \dfrac{3}{5}$

We can combine the denominators as the denominators are the same.

$\dfrac{2m - 4 + 3}{5}$

Finally, we can simplify -4 + 3.

$\dfrac{2m -1}{5}$

Therefore, the simplified expression is (2m - 1)/5.

Learn more about combining like terms: brainly.com/question/13080103

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$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

$p_v =2*P(Z>2)=0.0455$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the true mean differs from 24 at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X=25$ represent the sample mean

$\sigma=2$ represent the sample population deviation for the sample

$n=16$ sample size

$\mu_o =24$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 24, the system of hypothesis would be:

Null hypothesis: $\mu = 24$

Alternative hypothesis: $\mu \neq 24$

If we analyze the size for the sample is < 30 but we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{25-24}{\frac{2}{\sqrt{16}}}=2$

P-value

Since is a two sided test the p value would be:

$p_v =2*P(Z>2)=0.0455$

Conclusion

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